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Homework Help: Chain rule/multiple variables

  1. Jun 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Show z(x,y) = cos(xy) is a solution of

    (∂z/∂x)y + (∂z/dy)x = (x+y) ( (∂2z/∂x∂y) + xyz)

    (question also attached if it makes it clearer)

    3. The attempt at a solution

    ∂z= (∂z/∂x)ydx + (∂z/dy)xdy

    ∂z/∂x = -ysin(xy)
    ∂z/∂y = -xsin(xy)

    what does it mean show it is a solution? any tips appreciated

    Attached Files:

  2. jcsd
  3. Jun 3, 2014 #2


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    Gold Member

    It means that choice of z(x,y) satisfies the equation. I.e plug in z(x,y) into LHS and into the RHS and they should be equal.
  4. Jun 4, 2014 #3
    So for ##z(x,y) = \cos(xy) ##, what is ##\frac{∂^2z}{∂x∂y}##?
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